Quantifying and managing uncertainty in operational modal analysis

• Published in: Mechanical systems and signal processing 2018-03, Vol.102, p.139-157
• Main Authors: Au, Siu-Kui, Brownjohn, James M.W., Mottershead, John E.
• Format: Article
• Language: English
• Subjects: Ambient vibration test; Asymptotic methods; Asymptotics; BAYOMA; Channel noise; Configurations; Damping; Exact solutions; Forced vibration; Mastering; Mathematical analysis; Modal analysis; Operational modal analysis; Parameter identification; Parameter uncertainty; Signal to noise ratio; Standardization; Uncertainty; Uncertainty law; Vibration; Vibration measurement; Vibration tests
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2017.09.017

•Fundamental relationship between OMA uncertainty and test configuration.•Effect of test configuration is encapsulated in modal signal-to-noise ratio.•Simple charts for ambient vibration test planning. Operational modal analysis aims at identifying the modal properties (natural frequency, damping, etc.) of a structure using only the (output) vibration response measured under ambient conditions. Highly economical and feasible, it is becoming a common practice in full-scale vibration testing. In the absence of (input) loading information, however, the modal properties have significantly higher uncertainty than their counterparts identified from free or forced vibration (known input) tests. Mastering the relationship between identification uncertainty and test configuration is of great interest to both scientists and engineers, e.g., for achievable precision limits and test planning/budgeting. Addressing this challenge beyond the current state-of-the-art that are mostly concerned with identification algorithms, this work obtains closed form analytical expressions for the identification uncertainty (variance) of modal parameters that fundamentally explains the effect of test configuration. Collectively referred as ‘uncertainty laws’, these expressions are asymptotically correct for well-separated modes, small damping and long data; and are applicable under non-asymptotic situations. They provide a scientific basis for planning and standardization of ambient vibration tests, where factors such as channel noise, sensor number and location can be quantitatively accounted for. The work is reported comprehensively with verification through synthetic and experimental data (laboratory and field), scientific implications and practical guidelines for planning ambient vibration tests.